Shakespeare's Globe is something that you can walk by on the River Thames but you will never get the full effect unless you take the tour, which I recommend.
One of the most interesting facts that I find interesting is that the founder is American Sam Wanamaker. He died before the globe was completed.
The Globe you see today is not the original but they have done painstaking research to ensure that it is fashioned as the Globe was. The original was destroyed in a fire from a performance.
It has steep seating in 3 rows with room for people to stand in the centre under the sky (it is not fully enclosed.) There are no spotlights, microphones and the music is played on instruments from the time. It is the only thatched rooftop in London allowed after the Great Fire in London 1666.
You can also go to performances. Plays usually take place between May and September but tours are all year round.
All the Best!
American to Britain